Determining the area of a technical system stability in fuzzy sets terms

Abstract

Ensuring the stability of the technical systems functioning, including those in water transport, is an important area for the application of mathematical methods, including probabilistic and mathematical-statistical methods. The stochastic nature of disturbances affecting complex systems and worsening the level of stability of the latter should be reflected in the implemented human-machine control loops. One of the directions here is the accounting and use of (usually competing) expert assessments, on the one hand, and a reasonable definition of stability indicators, a choice from a variety of possibilities, on the other hand. From a general point of view of management theory, the method of using expert assessments developed in the paper can be considered as an integral part of the risk management problem that is being developed so far, mainly for economic systems and using only financial criteria. The concept of the minimum allowable efficiency of a technical system is introduced in the paper. On its basis, an approach in which the indicator of the stability of a technical system is linked to a system-wide criterion indicator of the quality of its functioning is implemented. The corresponding mathematical model as a problem of mathemati- cal programming is formulated. Approaches to its solution including for the nonconvex multiextremal case are discussed. A feature of the proposed approach to the definition of the integral indicator of the stability of the dynamics of a technical system is the use of expert assessments in determining the probable range of changes in the controlled variables of the optimization model, implemented as a mathematical programming problem, which logically leads to the use of fuzzy set theory. With the non-linearity of the objective functions and restrictions that arise in this case, the gradient method of searching for a conditional optimum is effective.